Question: 4 people can paint 5 walls in 47 minutes. How many minutes will it take for 7 people to paint 8 walls? Round to the nearest minute.
Answer: We know the following about the number of walls $w$ painted by $p$ people in $t$ minutes at a constant rate $r$ $w = r \cdot t \cdot p$ $\begin{align*}w &= 5\text{ walls}\\ p &= 4\text{ people}\\ t &= 47\text{ minutes}\end{align*}$ Substituting known values and solving for $r$ $r = \dfrac{w}{t \cdot p}= \dfrac{5}{47 \cdot 4} = \dfrac{5}{188}\text{ walls painted per minute per person}$ We can now calculate the amount of time to paint 8 walls with 7 people. $t = \dfrac{w}{r \cdot p} = \dfrac{8}{\dfrac{5}{188} \cdot 7} = \dfrac{8}{\dfrac{35}{188}} = \dfrac{1504}{35}\text{ minutes}$ $= 42 \dfrac{34}{35}\text{ minutes}$ Round to the nearest minute: $t = 43\text{ minutes}$